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pseudovector
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pseudovector

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Also known as axial vector, pseudovector quantity, space-oriented vector

thumb|right|A loop of wire (black), carrying a electric current|current I, creates a [[magnetic field B (blue). If the position and current of the wire are reflected across the plane indicated by the dashed line, the magnetic field it generates would not be reflected: Instead, it would be reflected and reversed. The position and current at any point in the wire are "true" vectors, but the magnetic field B is a pseudovector.]]

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13 sections
Contents
  • Physical examples
  • Details
  • Behavior under addition, subtraction, scalar multiplication
  • Behavior under cross products and curls
  • Examples
  • The right-hand rule
  • Formalization
  • Geometric algebra
  • Transformations in three dimensions
  • Note on usage
  • See also
  • Notes
  • References

thumb|right|A loop of wire (black), carrying a electric current|current I, creates a [[magnetic field B (blue). If the position and current of the wire are reflected across the plane indicated by the dashed line, the magnetic field it generates would not be reflected: Instead, it would be reflected and reversed. The position and current at any point in the wire are "true" vectors, but the magnetic field B is a pseudovector.]]

In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under continuous rigid transformations such as rotations or translations, but which does not transform like a vector under certain discontinuous rigid transformations such as reflections. For example, the angular velocity of a rotating object is a pseudovector because, when the object is reflected in a mirror, the reflected image rotates in such a way so that its angular velocity "vector" is not the mirror image of the angular velocity "vector" of the original object; for true vectors (also known as polar vectors), the reflection "vector" and the original "vector" must be mirror images.

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